In this paper, we first will show that for any space X and any Wallman sublattice of with , (, ) is the minimal quasi-F cover of X if and only if (, ) is a quasi-F cover of X and . Using this, if X is a locally weakly Lindelf space, the set { is a Wallman sublattice of with and is the minimal quasi-F cover of X}, when partially ordered by inclusion, has the minimal element and the maximal element . Finally, we will show that any Wallman sublattice of with , is -irreducible if and only if $\mathcal{A}